Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry</u>
- Area of a Rectangle: A = lw
<u>Algebra I</u>
- Exponential Property:

<u>Calculus</u>
Derivatives
Differentiating with respect to time
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Explanation:
<u>Step 1: Define</u>
Area is A = lw
2w = l
w = 300 m

<u>Step 2: Rewrite Equation</u>
- Substitute in <em>l</em>: A = (2w)w
- Multiply: A = 2w²
<u>Step 3: Differentiate</u>
<em>Differentiate the new area formula with respect to time.</em>
- Differentiate [Basic Power Rule]:

- Simplify:

<u>Step 4: Find Rate</u>
<em>Use defined variables</em>
- Substitute:

- Multiply:

- Multiply:

Answer:
F = 3750 N
Explanation:
Given that,
Pressure, P = 150 Pa
Area, a = 25m²
We need to find the force applied. We know that, pressure is equal to the force acting per unit area. It can be given by :

So, the required force is 3750 N.
Answer:
0.67 m/s
Explanation:
Mass of car 1, m₁ = 5000 kg
Mass of car 2, m₂ = 10,000 kg
Initial speed of car 1, u₁ = 2 m/s
Final speed of car 2, u₂ = 0 (at rest)
We need to find the final velocity of both cars when inelastic collision occurs. The momentum will remain conserved in case of inelastic collision. Using the conservation of momentum. Let V is the final speed.

So, after the inelastic collision, they will move with a speed of 0.67 m/s.
Hi there!
We know that:
U (Potential energy) = mgh
We are given the potential energy, so we can rearrange to solve for h (height):
U/mg = h
g = 9.81 m/s²
m = 30 g ⇒ 0.03 kg
0.062/(0.03 · 9.81) = 0.211 m